N-channel flow ratio controller calibration

ABSTRACT

Embodiments of the present invention generally relate to methods of controlling gas flow in etching chambers. The methods generally include splitting a single process gas supply source into multiple inputs of separate process chambers, such that each chamber processes substrates under uniform processing conditions. The method generally includes using a mass flow controller as a reference for calibrating a flow ratio controller. A span correction factor may be determined to account for the difference between the actual flow and the measured flow through the flow ratio controller. The span correction factors may be used to determine corrected set points for each channel of the flow controller using equations provided herein. Furthermore, the set points of the flow ratio controller may be made gas-independent using additional equations provided herein.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims benefit of U.S. Provisional Patent ApplicationSer. No. 61/293,545, filed Jan. 8, 2010, which is herein incorporated byreference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

Embodiments disclosed herein generally relate to processing a substratein an etch chamber.

2. Description of the Related Art

A chip manufacturing facility is composed of a broad spectrum oftechnologies. Cassettes containing semiconductor substrates are routedto various stations in a facility where they may be processed orinspected. Semiconductor processing generally involves the deposition ofmaterial onto and removal of material from substrates. Typical processesinclude chemical vapor deposition (CVD), physical vapor deposition(PVD), electroplating, chemical mechanical planarization (CMP), etching,and others.

One concern regarding substrate processing is substrate throughput.Generally, the greater the substrate throughput, the lower themanufacturing cost and therefore the lower the cost of the processedsubstrates. In order to increase substrate processing throughput, batchprocessing chambers have been developed. Batch processing allows severalsubstrates to be processed simultaneously using common fluids (such asprocess gases), chambers, processes, and the like, thereby decreasingequipment costs and increasing throughput. Ideally, batch-processingsystems expose each of the substrates to an identical processenvironment whereby each substrate simultaneously receives the sameprocess gases and plasma densities for uniform processing of the batch.Unfortunately, the processing within batch processing systems is hard tocontrol such that uniform processing occurs with respect to everysubstrate. Consequently, batch processing systems are notorious fornon-uniform processing of substrates. To achieve better process control,single chamber substrate processing systems were developed to conductsubstrate processing on a single substrate in a one-at-a-time-typefashion within an isolated process environment. Unfortunately, singlechamber substrate processing systems generally are not able to provideas high a throughput rate as batch processing systems, as each substratemust be sequentially processed.

Therefore, there is a need for a substrate processing system configuredto provide controllable etch uniformity of a single substrate system andimproved throughput characteristics of a batch processing system.

SUMMARY OF THE INVENTION

Embodiments of the present invention generally relate to methods ofcontrolling gas flow in etching chambers. The methods generally includesplitting a single process gas supply source into multiple inputs toseparate process chambers, such that each chamber processes substratesunder uniform processing conditions. The method generally includes usinga mass flow controller as a reference for calibrating a flow ratiocontroller. A span correction factor may be determined to account forthe difference between the actual flow and the measured flow through theflow ratio controller. The span correction factors may be used todetermine corrected set points for each channel of the flow controllerusing equations provided herein. Furthermore, the set points of the flowratio controller may be made gas-independent using additional equationsprovided herein.

In one embodiment, a method of calibrating a flow ratio controller for atandem etching chamber includes setting a first channel of a flow ratiocontroller coupled to the process gas supply to a 100 percent set point.All remaining channels of the flow ratio controller are set to a zeropercent set point, and all downstream isolation valves for the remainingchannels of the flow ratio controller that are set at the zero percentset point are closed. The flow of a mass flow controller is set equal tothe flow of the 100 percent set point of the first channel. The flow ofa process gas through the flow ratio controller is allowed to stabilize,and a span correction factor for the flow of the process gas through thefirst channel of the flow ratio controller is calculated. Repeatingsimilar steps, a span correction factor for the flow of the process gasthrough the remaining channels of the flow ratio controller iscalculated. A corrected set point for each channel of the flow ratiocontroller is then calculated.

In another embodiment, a method of calibrating a flow ratio controllerfor a tandem etching chamber includes determining a span correctionfactor for a first channel of the flow ratio controller, which comprisessetting the first channel of the flow ratio controller coupled to theprocess gas supply to a 100 percent set point. All remaining channels ofthe flow ratio controller are set to a zero percent set point, and alldownstream isolation valves for the remaining channels of the flow ratiocontroller that are set at the zero percent set point are closed. Theflow of a mass flow controller is set equal to the flow of the 100percent set point of the first channel. The flow of a process gasthrough the first channel of the flow ratio controller is allowed tostabilize, and the flow of the process gas through the first channel ofthe flow ratio controller is measured for at least about 10evenly-spaced time intervals. A span correction factor is calculated forthe flow of the process gas through the first channel of the flow ratiocontroller. The span correction factors for the remaining channels ofthe flow ratio controller are calculated, and the corrected set pointsfor each channel of the flow ratio controller are determined using theequation:

${cSP}_{i} = {\frac{S\; P_{i}}{C\; F_{i}}*{\left( {\sum\limits_{i}^{n}\frac{S\; P_{i}}{C\; F_{i}}} \right)^{- 1}.}}$

In another embodiment, a method of calibrating a flow ratio controllerfor a tandem etching chamber includes splitting a process gas supplyinto four gas supply lines. A first gas line and second gas line arecoupled to a first process chamber, and a third gas line and fourth gasline are coupled to a second process chamber. Each gas line is coupledto a distinct channel of a flow ratio controller. A corrected set pointfor the first, second, third, and fourth channels of the flow ratiocontroller are determined using the equation:

${cSP}_{i} = {\frac{S\; P_{i}}{C\; F_{i}}*{\left( {\sum\limits_{i}^{n}\frac{S\; P_{i}}{C\; F_{i}}} \right)^{- 1}.}}$Gas-independent precision correction factors for the first, second,third, and fourth channels of the flow ratio controller are determinedusing the equations:

${P\; C\; F_{1}} = \frac{4}{1 + {\frac{1}{C\; F_{1}}\left( {{C\; F_{2}} + {C\; F_{3}} + {C\; F_{4}}} \right)}}$${P\; C\; F_{2}} = \frac{4}{1 + {\frac{1}{C\; F_{2}}\left( {{C\; F_{1}} + {C\; F_{3}} + {C\; F_{4}}} \right)}}$${P\; C\; F_{3}} = \frac{4}{1 + {\frac{1}{C\; F_{3}}\left( {{C\; F_{1}} + {C\; F_{2}} + {C\; F_{4}}} \right)}}$${P\; C\; F_{4}} = {\frac{4}{1 + {\frac{1}{C\; F_{4}}\left( {{C\; F_{1}} + {C\; F_{2}} + {C\; F_{3}}} \right)}}.}$Set points for the first, second, third, and fourth channels of the flowratio controller are recalculated using the gas-independent precisioncorrection factors and the equation:

${cSP}_{i} = {\frac{S\; P_{i}}{P\; C\; F_{i}}*{\left( {\sum\limits_{i}^{n}\frac{S\; P_{i}}{P\; C\; F_{i}}} \right)^{- 1}.}}$

BRIEF DESCRIPTION OF THE DRAWINGS

So that the manner in which the above recited features of the presentinvention can be understood in detail, a more particular description ofthe invention, briefly summarized above, may be had by reference toembodiments, some of which are illustrated in the appended drawings. Itis to be noted, however, that the appended drawings illustrate onlytypical embodiments of this invention and are therefore not to beconsidered limiting of its scope, for the invention may admit to otherequally effective embodiments.

FIG. 1 is a schematic of a tandem chamber etch system.

FIG. 2 is a sectional view of a first and second process chamber of atandem processing chamber.

FIG. 3 is a perspective view of a lid of a first and second processchamber of a tandem processing chamber.

FIG. 4 is a bottom view of a gas distributor.

FIG. 5 is flow chart describing a method for determining a correctionfactor for a flow ratio controller channel.

To facilitate understanding, identical reference numerals have beenused, where possible, to designate identical elements that are common tothe figures. It is contemplated that elements and features of oneembodiment may be beneficially incorporated in other embodiments withoutfurther recitation.

DETAILED DESCRIPTION

Embodiments of the present invention generally relate to methods ofcontrolling gas flow in etching chambers. The methods generally includesplitting a single process gas supply source into multiple inputs ofseparate process chambers, such that each chamber processes substratesunder uniform processing conditions. The method generally includes usinga mass flow controller as a reference for calibrating a flow ratiocontroller. A span correction factor may be determined to account forthe difference between the actual flow and the measured flow through theflow ratio controller. The span correction factors may be used todetermine corrected set points for each channel of the flow controllerusing equations provided herein. Furthermore, the set points of the flowratio controller may be made gas-independent using additional equationsprovided herein.

Embodiments discussed herein may be practiced in any tandem chambersubstrate processing system. For example, embodiments disclosed hereinmay be practiced in the PRODUCER® Etch processing chamber available fromApplied Materials, Inc., Santa Clara, Calif. It is to be understood thatthe embodiments discussed herein may be practiced in other processingsystems, including those sold by other manufacturers.

FIG. 1 illustrates a plan view of a tandem chamber etch system 100 inwhich the embodiments may practiced. The system 100 is generally aself-contained system having processing utilities supported on amainframe structure that can be easily installed and provides a quickstart up for operation. System 100 generally includes four differentregions, namely, a front-end staging area 102, a load lock chamber 112,and a transfer chamber 104 in communication with a plurality of tandemprocessing chambers 106 through isolation valves 110. Front-end stagingarea 102, which is generally known as a factory interface or minienvironment, generally includes an enclosure having at least onesubstrate containing cassette 109 positioned in communication therewithvia a pod loader. The system 100 may also include a pair of front-endsubstrate transfer robots 114 which may generally be single-arm robotsconfigured to move substrates between the front-end staging area 102 andthe load lock chamber 112. The pair of front-end substrate transferrobots 114 are generally positioned proximate cassettes 109 and areconfigured to remove substrates therefrom for processing, as well asposition substrates therein once processing of the substrates iscomplete.

Although two cassettes 109 are shown, the system 100 is not limited toany particular number of cassettes 109. For example, the system 100 mayutilize a stackable substrate cassette feeder assembly (not shown). Thestackable substrate feeder assembly may be configured to store aplurality of cassettes 109 in a vertical stack and individually deliverthe cassettes 109 to outer cassette locations/pod loaders when needed.The front-end staging area 102 is selectively in communication with theload lock chamber 112 through, for example, a selectively actuated valve(not shown). Additionally, load lock chamber 112 may also be selectivelyin communication with the transfer chamber 104 via another selectivelyactuated valve. Therefore, the load lock chamber 112 may operate toisolate the interior of the substrate transfer chamber 104 from theinterior of the front-end enclosure 102 during the process oftransferring one or more substrates into the transfer chamber 104 forprocessing. The load lock chamber 112 may be a side-by-side substratetype chamber, a single substrate type chamber, or multi-substrate typeload lock chamber.

As illustrated in FIG. 1, a substrate transfer robot 111 may becentrally positioned in the interior portion of the transfer chamber104. The substrate transfer robot 111 is generally configured to receivesubstrates from the load lock chamber 112 and transport the substratesreceived therefrom to one of the tandem processing chambers 106positioned about the perimeter of the transfer chamber 104.Additionally, the substrate transfer robot 111 is generally configuredto transport substrates between the respective tandem processingchambers 106, as well as from the tandem processing chambers 106 backinto the load lock chamber 112. The substrate transfer robot 111generally includes an end effector configured to support two substratesthereon simultaneously. The end effector may include two supportsurfaces generally aligned in a single plane to hold the substratesthereon. Additionally, the end effector of the substrate transfer robot111 is selectively extendable, while the base is rotatable, which mayallow the end effector access to the interior portion of any of thetandem processing chambers 106, the load lock chamber 112, and/or anyother chamber positioned around the perimeter of the transfer chamber104.

FIG. 2 illustrates a sectional view of the first and second processchambers of a tandem processing chamber 206. One tandem processingchamber 206 comprises two process chambers 201 a, 201 b. Each of therespective first and second process chambers 201 a, 201 b may include anupper and lower portion 219, 231, wherein the upper portion 219generally includes upper electrode assemblies 218 a, 218 b and the lowerportion 231 generally includes a loading region (not shown) to permitentry and exit of substrates into the respective process chambers 201 a,201 b. Each of the respective first and second process chambers 201 a,201 b include sidewalls 205 a, 205 b, interior wall 207, a bottom 213,and a lid 215 disposed thereon. Gas distributors 222 a, 222 b aredisposed within process chambers 201 a, 201 b. The sidewall 205 a,interior wall 207 and gas distributor 222 a define a first processingregion 203 a. The sidewall 205 b, interior wall 207 and gas distributor222 b define a second processing region 203 b. The interior wall 207 isshared between the respective first and second process chambers 201 a,201 b and isolates the processing environment of the processing regions203 a, 203 b from contamination. However, in some embodiments, theprocessing regions 203 a, 203 b defined in the respective processchambers 201 a, 201 b, while remaining process isolated, may share acommon pressure. For example, the lower portion of interior wall 207 mayallow the respective first and second process chambers 201 a, 201 b tocommunicate with each other by way of central pumping plenum 217.

The lower portion of interior wall 207 is defined by a central pumpingplenum 217. The lid 215 may include one configuration of gasdistribution assemblies 216 a, 216 b including a showerhead 222 a, 222 bconfigured to dispense a gas into the respective processing regions 203a, 203 b. The lid 215 is generally attached to the tandem processingchamber 206 using a hinge. Gas lines coupled to the lid 215 areconfigured to allow the lid 215 to open upon its hinges. The hinged lid215 allows for convenient access to the chamber components. A cover 261may be disposed on the lid 215 to protect components disposed thereon.

To provide process analysis, windows 287 a, 287 b may be disposed withineach sidewall 205 a, 205 b and optically aligned with openings 284 a,284 b disposed within the chamber liner. Each window 287 a, 287 b may becomposed of any optically clear material adapted to withstand a processenvironment while providing an optical pathway for optical detectors 288a, 288 b disposed adjacent each process chamber 201 a, 201 b. Theoptical detectors 288 a, 288 b may be configured to optically receiveand process optical signals from within the respective processingregions 203 a, 203 b and provide data representative of chamber orsubstrate conditions to a process controller (not shown).

Optical windows 287 a, 287 b, optical detectors 288 a, 288 b, and aprocess controller collectively form process analysis systems 289 a, 289b. During operation, optical signals may be processed by the processanalysis systems 289 a, 289 b to detect etching conditions for eachprocess chamber 201 a, 201 b. To detect an etching process endpoint, aprocess endpoint measurement may be stored, for example, and compared bythe process controller to a current measurement. Once the processanalysis systems 289 a, 289 b detect an optical signal from a processchamber 201 a, 201 b, the process controller may provide an endpointindication to a user.

Process chambers 201 a, 201 b also include substrate supports 208 a, 208b. When the substrate supports 208 a, 208 b are in a processingposition, the upper portion 219 of process chambers 201 a, 201 b andsubstrate supports 208 a, 208 b generally define the respective isolatedprocessing regions 203 a, 203 b. Therefore, in combination, thesidewalls 205 a, 205 b, interior wall 207, substrate supports 208 a, 208b, and the lid 215 provide process isolation between the processingregions 203 a, 203 b.

The volume of the processing regions 203 a, 203 b may vary with theposition of the substrate supports 208 a, 208 b relative to the lowerboundary of the lid 215. In one configuration, substrates may bepositioned on the substrate supports 208 a, 208 b through gate valve 110(See FIG. 1). The substrates can be lifted off the substrate supports208 a, 208 b with lift pins, and a robot blade may enter the processingregions 203 a, 203 b to engage the substrates for removal. Similarly,with the substrate supports 208 a, 208 b in a lowered positioned,substrates may be placed thereon for processing. Thereafter, thesubstrate supports 208 a, 208 b may be vertically moved into aprocessing position, e.g., a position where the upper surface of thesubstrate supports 208 a, 208 b are positioned proximate to therespective processing region 203 a, 203 b.

In one embodiment, the substrate supports 208 a, 208 b may compriseelectrostatic chucks to provide a stable working position for asubstrate supported thereon. First and second chuck power supplies 244a, 244 b may be coupled to the electrostatic chucks, and may be used toproduce an electrostatic field proximate to the electrostatic chucks tohold the substrates thereto. The first and second chuck power supplies244 a, 244 b may be DC supplies configured to provide an electrostaticfield between the electrostatic chucks and the substrates. Toelectrically bias plasma toward and away from the substrate supports 208a, 208 b, a first electrical bias source 254 a and second electricalbias source 254 b may be coupled to the substrate supports 208 a, 208 b.

The lid 215 may have other plasma generation devices disposed adjacentthereto. In one embodiment, the upper electrode assemblies 218 a, 218 bmay be configured with RF coils (not shown). The coils may be coupled tothe first and second RF sources 250 a, 250 b through respective matchingnetworks 251 a, 251 b, to inductively couple RF energy into the plasmaprocessing regions 203 a, 203 b. The RF power supply controller 249 iscoupled to RF power supplies 250 a, 250 b to provide output signalcontrol including power level control, phase control (locking) and/orfrequency control (locking).

The lower portion 231 of the respective first and second processchambers 201 a, 201 b may also include a commonly shared adjacentchamber region of each chamber defined by a central pumping plenum 217.The central pumping plenum 217 may be in fluid communication with acommon vacuum source 220 through a pumping valve 221. Generally, thecentral pumping plenum 217 includes two sections defined by thesidewalls 205 a, 205 b that are combined with an output port 230 influid communication with the pumping valve 221. The two sections may beformed as part of the lower portion 231 of each process chamber 201 a,201 b. While the central pumping plenum 217 may be formed integral tothe lower portion 231 of the first and second process chambers 201 a,201 b, it is contemplated that the central pumping plenum 217 may be aseparate body coupled thereto. In a gas purge or vacuum process, thepumping valve 221 couples the vacuum source 220 to the output port 230.Therefore, the central pumping plenum 217 is generally configured tomaintain the respective chambers 201 a, 201 b, and more particularly,the respective processing regions 203 a, 203 b, at a pressure desiredfor semiconductor processing while allow for rapid removal of wastegases using a single vacuum source 220.

In one configuration, the output port 230 is positioned a distance fromthe processing regions 203 a, 203 b such as to minimize RF energytherein, thereby minimizing striking a plasma in the exhaust gases beingflushed from the processing chambers 201 a, 201 b. For example, theoutput port 230 may be positioned at a distance from the substratesupports 208 a, 208 b and processing regions 203 a, 203 b that issufficiently far to minimize RF energy within the output port 230.

FIG. 3 is a perspective view of a lid 315 of first and second processchambers of a tandem processing chamber 206. The lid 315 includes upperelectrode assemblies 318 a, 318 b. The lid 315 and/or first and secondprocess chambers may include cooling passages (not shown) that circulatecoolant received from an upper coolant input/output port 385. The upperelectrode assemblies 318 a, 318 b are disposed adjacent the processingregions and adapted to provide RF energy to respective processingregions. To provide thermal control to the upper electrode assemblies318 a, 318 b, cooling channels for the first and second upper electrodeassemblies 318 a, 318 b may be coupled to an external coolant source(not shown) by a first and second coolant inputs 391 a, 391 b.

The upper electrode assemblies 318 a, 318 b may include an RF shield 399mounted between the first and second upper electrode assemblies 318 a,318 b to minimize RF leakage by isolating electromagnetic fieldstherebetween. The RF shield 399 may include materials adapted to absorbor reflect RF energy. For example, RF shield 399 may include metals suchas steel and aluminum, and may also include electromagnetic insulatingmaterials. The RF shield 399 may be configured to span the width of thelid 315 and may extend to the top of the cover of the apparatus. Toprovide additional RF isolation, the shield member 399 may include an RFgasket (not shown) disposed between the shield member 399 and the lid315.

A gas flow measuring device such as a mass flow controller (MFC, notshown) is used in conjunction with a flow ratio controller to controlthe amount of gas flow to each processing region. Measured gas flow isprovided to each processing region through the gas distributionassemblies 316 a, 316 b. In the embodiment of FIG. 3, the MFC and thegas flow ratio controllers are disposed within gas panel 362. It iscontemplated, however, that the MFC and the flow ratio controllers maybe disposed outside of the gas panel 362.

A process gas supply 368 is coupled to gas panel 362. Additional processgas supplies (not shown) may be coupled to gas panel 362. Gas panel 362includes the MFC to regulate the amount of process gas supplied fromprocess gas supply 368 to the process chambers through gas supply lines363 a, 363 b, 364 a, 364 b. The MFC is disposed between process gassupply 368, and gas supply lines 363 a, 363 b, 364 a, 364 b. Gas supplylines 363 a, 363 b, 364 a, 364 b are in fluid communication with theMFC.

Gas supply lines 363 a, 363 b, 364 a, 364 b are configured to allow foropening and closing of chamber lid 315 upon its hinges. Gas supply lines363 a, 363 b are coupled to an interior zone of the gas distributorswhile gas supply lines 364 a, 364 b are coupled to an outer zone of thegas distributors. Therefore, the apparatus of FIG. 3 allows a singleprocess gas supply source 368 to be divided between each process chamberof a tandem processing chamber, as well as each zone of the gasdistributors. This results in a single gas source being split andregulated four ways in the embodiment of FIG. 3. In other embodiments, asingle gas supply source may be split and regulated in more than 4 ways,such as 6, 8, 10 or 12 different ways. Regardless of the number of gasline splits, embodiments herein allow for the regulation of the gas flowthrough the gas lines using a single MFC.

FIG. 4 shows a bottom view of the gas distributor 422 according to oneembodiment. Gas distributor 422 is positioned centrally in the processchambers. Openings 472 are positioned centrally in the process chambersabove the substrate support and substrate. Gas distributor 422 comprisesa first zone centrally-located having holes 472, through which processgas is provided from the gas supply lines to the processing regions. Gasdistributor 422 also comprises an outer zone disposed circumferentiallyaround the central zone. The outer zone has holes 474 through whichprocess gas is provide from the gas supply lines to processing regions.While the gas distributor of FIG. 4 depicts four holes in the centralzone, and eight holes in the outer zone, gas distributor 422 can includeany number of holes in each zone, depending on the application and thesize of the substrates to be processed in the process chambers.

The multiple zones of gas distributor 422 allow for tuning of processgas flow with respect to the radial etching rate of a substrate. Forexample, if the center of a substrate is etched at a rate faster thanthe perimeter of the substrate, then process gas supplied through thecentral zone holes 472 may be reduced, or the amount of process gassupplied to the outer zone holes 474 may be increased. This allows forthe etching rate across the substrate to become substantially equal,thus producing a more uniform substrate. Since different gas flows canbe provided through the central and outer zones, it is important thatthe gas flows be accurately measured and regulated to ensure desiredsubstrate processing.

Since a single gas supply could be split between two processing chambers(and further into two gas distribution zones per process chamber) it maybe important to ensure that each process chamber receives substantiallythe same amount of process gas. When similar amounts of process gas areprovided to the process chambers, the process chambers are able toprocess substrates under substantially similar operating conditions.Similar operating conditions among the process chambers allows forprocess uniformity among processed substrates. If a single gas supplyline has any error in its flow rate to the chamber, process uniformitycan be affected. Therefore, the error in flow rate needs to becorrected, and other gas supply lines should take into account anycorrection provided to adjacent gas lines.

One embodiment of the invention uses a MFC to calibrate the channels ofa flow ratio controller (FRC), with each channel of the FRC coupled to agas supply line. The FRC is responsible for regulating the amount ofprocess supply gas disposed through the central zone and the outer zoneof the gas distributors 422 disposed in each process chamber. Themethods of the present invention allow for accurate gas flow controlwith a reduced number of mass flow controllers. For example, a MFC isnot necessary for every channel of the FRC.

FIG. 5 is flow chart 500 representing one embodiment of the invention.Flow chart 500 describes how to derive channel correction factors forflow rate errors with a reduced number of MFCs. Flow chart 500 begins atstep 502. At step 502, all FRC channels are zeroed under vacuum. All FRCchannels should be zeroed on a regular basis by requesting a zeroservice from the FRC device, subsequent to a manifold leak check.However, if recently zeroed, this step may be optional.

At step 504, one of the channels of the FRC is set to the 100 percentset point (e.g., channel full scale), and all other FRC channels are setto the zero percent set point. For example, channel 1 may be set to the100 percent set point. The 100 percent set point is the set pointallowing maximum gas passage through the FRC. At step 506, alldownstream isolation valves on channels with a zero percent set pointare closed. This allows for all the gas measured by the MFC to flowthrough and be measured by a single FRC channel, for example FRCchannel 1. At step 508, The MFC is set to provide a gas flowcorresponding to the 100 percent channel flow of the FRC. For example,if the FRC of channel 1 at 100 percent set point can flow 1000 SCCM ofN₂ gas, then the MFC is also configured to flow 1000 SCCM of N₂ gas tochannel 1. MFCs utilized in embodiments of the present invention can beconfigured to flow any amount of process gas as is required by a processrecipe. For example, an MFC may be configured to flow a process gaswithin a range from about 100 SCCM to about 5000 SCCM of N₂ gas, such asabout 500 SCCM to about 1500 SCCM, or about 800 SCCM to about 1200 SCCM.It is contemplated that MFCs adapted to flow greater or lesser amountsof process gas may be utilized.

At step 510, the gas flow through the MFC and the FRC is allowed tostabilize. For example, the gas is allowed to flow for at least about 50seconds. At step 512, after the gas flow has stabilized, the MFCreported flow and FRC reported flow are recorded over about a 10 secondinterval, with a minimum of 10 evenly-spaced samples being taken. Forexample, 25, 50, or 100 samples may be taken. At step 514, the mean andstandard deviation between the MFC flow and FRC flow can be calculatedfor each of the evenly-spaced samples. If the standard deviation isgreater than about 0.5 percent, this indicatives that the flow was notstabilized, and step 510 may need to be repeated. If step 510 needs tobe repeated about three times, this could signal an issue with the MFCor FRC, which may require additional troubleshooting or replacement ofthe MFC or FRC.

At step 516, span correction factors are calculated using the mean flowvalue calculated at step 514 (See Equation 1). At step 518, steps 504through 516 are performed for the remaining FRC channels (e.g., thosecoupled to the remaining gas supply lines).

Referring back to step 516, the span correction factors can becalculated in the following manner. The span correction factor (CF_(i))is defined by the following equation:

$\begin{matrix}{{CFi} = \frac{{Single}\mspace{14mu}{Channel}\mspace{14mu}(i)\mspace{14mu}{Actual}\mspace{14mu}{Flow}}{{Single}\mspace{14mu}{Channel}\mspace{14mu}(i)\mspace{14mu}{Reading}}} & \left( {{Equation}\mspace{14mu} 1} \right)\end{matrix}$

The span correction factor (CF_(i)) accounts for span error. The SingleChannel Actual Flow represents the MFC flow in SCCM from step 508 above,and the Single Channel Reading represents the mean FRC flow from step514 for the respective channel i. The span correction factor CF_(i)accounts for the difference in actual flow rate of channel and themeasured flow rate. However, since a single gas supply is being splitinto multiple channels, all channels must take into account thecorrection factors of other channels.

Using the span correction factors from Equation 1 (the single channelcorrection factor), the corrected set points for the FRCs can be derivedusing Equation 2, which is the set point for each channel of the FRC,taking into account correction factors applied to other channels of theFRC.

$\begin{matrix}{{cSP}_{i} = {\frac{{SP}_{i}}{C\; F_{i}}*\left( {\sum\limits_{i}^{n}\frac{{SP}_{i}}{C\; F_{i}}} \right)^{- 1}}} & \left( {{Equation}\mspace{14mu} 2} \right)\end{matrix}$

The corrected set points are calculated from an “m×m” system of linearequations (m number of rows by m number of columns), where m=n+1, andn=the number of channels of the FRC coupling gas supply lines to theprocess chambers 201 a, 201 b (See FIG. 2). In the embodiment of FIG. 3,n=4, representing gas supply lines 363 a, 363 b, 364 a, 364 b. ForEquation 2, cSP_(i) is the calculated corrected set point of respectivechannel i, SP_(i) is the set point for channel i, and CF_(i) is the spancorrection factor for channel i, calculated from Equation 1.

The span correction factor (CF_(i)) provides for correction between theactual flow of the MFC, and the set point of the FRC through a singlechannel. The calculated corrected set point (cSP_(i)) accounts for thesummation of the span corrections, taking into account the spancorrection factor of adjacent FRCs. The cSP_(i) provides the set pointat which the FRC should be set to deliver the desired amount of processgas to the chamber, accounting for deviation of the respective channelas well as adjacent channels of the FRC. Since one process gas supply isdivided among four gas lines through four channels of an FRC (in FIG. 3for example), any correction necessary at one FRC channel may requirecorrection at another channel as well. As discussed above, it may beimportant that all process chambers receive the same amount of processgas to ensure substrate throughput uniformity. Thus, if a first channelof the FRC requires a span correction factor (CF_(i)), then otherchannels must take into the first channel's correction factor also. Thisensures equal process gas distribution between process chambers.Equation 2 adequately accounts for all channel correction factors whenderiving the corrected set point for each respective channel, using areduced number of MFCs.

One skilled in the art can appreciate that the above equations can beapplied to etch chambers using any number of process gas lines and FRCchannels. A brief discussion of how FRCs operate will allow this tobecome more clear. At any point in time during the FRC operation, theFRC control algorithm reads the total incoming flow as the sum ofmeasured flow rate by each of its channels “QinRd”. It is noted thateach FRC may have any number of incoming and outgoing flows, however,for purposes of clarity, embodiments herein will be discussed withreference to a FRC with a single incoming flow and four outgoingchannels.

Regarding QinRd, this total flow reading is used to determine thedesired flow set point for a channel by multiplying QinRd with thepercent-set point for the respective channel. Due to span errors, QinRdis not constant, even while the actual incoming flow is constant. Insteady state, QinRd is a function of the set point for each channel.

QinRd is defined as follows:

$\begin{matrix}{{QinRD} = {{QinActual}*\left( {\sum\limits_{i}^{n}\left( {{SP}_{i}*C\; F_{i}} \right)^{- 1}} \right.}} & \left( {{Equation}\mspace{14mu} 3} \right)\end{matrix}$SP_(i) is the set point for channel i, CF_(i) is span correction factorfor channel i, QinRd is the total incoming flow reading as function ofSP_(i) for all channels of the FRC, and QinActual is the actual totalincoming flow. By rearranging Equation 3, we can arrive at Equation 4,which is the actual flow per channel.QinActual(i)=QinRD*SP_(i)*CF_(i)  (Equation 4)

Furthermore, the desired actual flow for a channel is equal to the setpoint multiplied by the total incoming actual flow. To achieve balancedflow, the total incoming flow as measured by the sum of all FRCchannels, multiplied by the corrected set point and the span correctionfactor must equal the actual flow for a channel. Thus, Equation 5 holdstrue for every set point.cSP_(i) *QinRD_(c)*CF_(i)*SP_(i) *QinActual  (Equation 5)

For Equation 5, Sp_(i) is the set point for channel i (in percentageflow), cSP_(i) is the corrected set point for channel i (in percentageflow) derived from Equation 2 above, QinRdc is the total incoming flowreading as a function of cSP_(i) for all channels of the FRC, QinActualis the actual total incoming flow, and CF_(i) is span correction factorderived from Equation 1. QinRdc is an unknown variable in Equation 5,and is a function of the span errors and corrected set points of allchannels of the FRC for a particular actual flow. To solve the aboveequation, and additional equation is required. Since the sum of all setpoints is always 100%, Equation 6 is true.

$\begin{matrix}{{\sum\limits_{i}^{n}{cSP}_{i}} = {100\%}} & \left( {{Equation}\mspace{14mu} 6} \right)\end{matrix}$

The corrected set point is calculated from an “m×m” system of linearequations, where m=n+1, and n=the number of channels of the FRC havinggas lines coupled to the process chambers. Equation 7 represents oneexample of an “m×m” matrix for a four-channel FRC. The columns representcSP₁, cSP₂, cSP₃, cSP₄, and QinRd, respectively. Solving the matrixyields one solution for each of the 5 unknowns, and derives Equation 2,above, which can be used to calculate the corrected set point for eachchannel of an n-channel FRC.

$\begin{matrix}\left\langle \begin{matrix}{C\; F_{1}} & 0 & 0 & 0 & {{SP}_{1}*{QinActual}} & 0 \\0 & {C\; F_{2}} & 0 & 0 & {{SP}_{2}*{QinActual}} & 0 \\0 & 0 & {C\; F_{3}} & 0 & {{SP}_{3}*{QinActual}} & 0 \\0 & 0 & 0 & {C\; F_{4}} & {{SP}_{4}*{QinActual}} & 0 \\1 & 1 & 1 & 1 & 0 & 1\end{matrix} \right\rangle & \left( {{Equation}\mspace{14mu} 7} \right)\end{matrix}$

To verify the results of Equation 2, one can determine the totalincoming flow as read by all channels of the FRC (e.g., QinRd_(c)) withEquation 8.

$\begin{matrix}\left. {{QinRd}_{c} = {{QinActual}/\left( {\sum\limits_{i}^{n}{{cSP}_{i}*C\; F_{i}}} \right)}} \right) & \left( {{Equation}\mspace{14mu} 8} \right)\end{matrix}$

Equation 8 can be rearranged to form Equation 9, which yields anexpression for the actual incoming flow. The calculated sum of the allactual flows for all channels as calculated by Equation 2 must equal theactual flow of the MFC (Equation 8).

$\begin{matrix}\left. {{QinActual} - {{QinRd}_{c}*\left( {\sum\limits_{i}^{n}{{cSP}_{i}*C\; F_{i}}} \right)}} \right) & \left( {{Equation}\mspace{14mu} 9} \right)\end{matrix}$

Table 1 shows a calculation example for a corrected set pointcalculation and verification of the result for a 4-channel FRC. Thesingle channel actual flow and the single channel reading can be used todetermine the span correction factor using Equation 1. In the bottomsection of Table 1, “setpoint %” corresponds to the desired percentageof gas flow of the respective channel. However, due to the difference inactual flow of the channel versus the single channel reading of therespective channel, the flow rate is inaccurate. The span correctionfactor derived using Equation 1 provides a method for determining acorrected set point for each channel using Equation 2. As can be seenbelow, the corrected set point can vary widely from the initial setpoint.

Embodiments described above allow a processing system user to accuratelyprogram gas flow set points, which improves process uniformity inseparate chambers and increases substrate throughput. Additionally,embodiments described above provide a method for tuning process gas flowusing a reduced number of MFCs, which reduces the overall cost of theprocessing system.

TABLE 1 ch1 ch2 ch3 ch4 Total FRC Span Verification Single ChannelActual Flow 100 98 100 100 398 (SCCM) Single Channel Reading (SCCM) 11067 180 112 469 Reading Error 10 −31 80 12 71 Span Slope 1.1000000.683673 1.800000 1.120000 Span Correction Factor 0.909091 1.462690.55556 0.89286 Calculation of Corrected Set Point Set Point Percent10.00% 40.00% 10.00% 40.00% 100.00% SPi/CFi 0.11 0.27 0.18 0.45 1.01Corrected Set Point 10.88% 27.04% 17.80% 44.29% 10.00% Cannel ActualFlow (SCCM) 30.00 120.00 30.00 120.00 300.00 Channel Reading (SCCM)33.00 82.04 54.00 134.00 303.44

As can be seen in Table 1, the FRC actual flow as measured by the MFCfor channel 1 was 100 SCCM of N₂ gas. However, the FRC read the incomingflow for channel 1 as 110 SCCM of N₂ gas, which resulted in an error of10 SCCM of N₂ gas through channel 1. Using Equation 1, a span correctionfactor of 0.909091 was derived. The FRC actual flow as measured by theMFC for channel 2 was 98 SCCM of N₂ gas. The FRC read the incoming flowfor channel 2 as 67 SCCM of N₂ gas, which resulted in an error of 31SCCM of N₂ gas through channel 2. Using Equation 1, a span correctionfactor of 0.89286 was derived.

The FRC actual flow as measured by the MFC for channel 3 was 100 SCCM ofN₂ gas. The FRC read the incoming flow for channel 3 as 180 SCCM of N₂gas, which resulted in an error of 80 SCCM of N₂ gas through channel 3.Using Equation 1, a span correction factor of 0.55556 was derived. TheFRC actual flow as measured by the MFC for channel 4 was 100 SCCM of N₂gas. The FRC read the incoming flow for channel 4 as 112 SCCM of N₂ gas,which resulted in an error of 12 SCCM of N₂ gas through channel 4. UsingEquation 1, a span correction factor of 0.909091 was derived. The totalflow through all four channels combined was 398 SCCM of N₂ gas, althoughthe FRC was reading a flow rate of 469 SCCM of N₂ gas. This results inan error of 71 SCCM of N₂ gas.

In the second part of Table 1, QinActual is equal to 300 SCCM of N₂ gas,and QinRd is 303.44 SCCM of N₂ gas. In Table 1, corrected set points aredetermined for channels 1 through 4 of the FRC. Channel 1 set point isinitially desired to be 10 percent of QinActual (300 SCCM of N₂ gas).However, because channel 1 is reading 110 SCCM of N₂ gas when it is onlyflowing 100 SCCM of N₂, channel 1 would need to read 33 SCCM of N₂ gasto flow 30 SCCM of N₂ gas, e.g., the set point would need to bedifferent than the desired flow rate. Channel 2 is desired to be set at40 percent of QinActual, but since it is flowing 98 SCCM of N₂ gas whenit is reading 67 SCCM of N₂ gas, the set point for channel 2 must becorrected also. Similarly, since the actual flows for channels 3 and 4differ from the readings of channels 3 and 4, the set points will alsoproduce different gas flows than desired. Therefore, it is necessary touse Equation 2 to calculate the corrected set points based from the spancorrection factors for each channel.

The corrected set points for channel 1 through channel 4 (10.88 percent,27.04 percent, 17.80 percent, and 44.29 percent, respectively) indicatethe set points the FRC channels should be set at to correct thedifference in actual versus read flow rate for all the channels. Oncecorrected, the actual flow rates through the channels will be equal tothe desired flow rates. In Table 1, the desired flow rates of channels 1through channels four are 10 percent, 40 percent, 10 percent, and 40percent of 300 SCCM of N₂ gas, respectively.

Furthermore, one channel cannot simply be corrected without taking intoaccount the remaining channels. Since QinActual remains nearly constant,the change in flow rate of a single isolated channel would cause thecorrected difference in the flow rate to be provided to the otherchannels. However, Equation 2 accurately takes into account the changein flow rate of all channels, and reduces the overall error of the flowrate (QinActual versus QinRd) to about 1 percent in the example ofTable 1. In the upper half of Table 1, prior to using the corrected setpoints, the overall flow rate had an error of 71 SCCM of N₂ gas(approximately 24 percent). While using the corrected set points, theoverall flow rate had only an error of about 3 SCCM of N₂ gas(approximately 1%).

Table 1 is derived using diatomic nitrogen (N₂) as the process gas.Consequently, the FRCs were also calibrated assuming diatomic nitrogenas the process gas. If another process gas were used, normally the FRCswould need to be recalibrated to account for the new process gas.However, by implementing an additional set of correction factors, termedgas-independent precision correction factors, multiple process gassescan be regulated by a single FRC without recalibration. Thegas-independent precision correction factors allow the FRC to operate ina gas-independent manner.

The use of gas-independent precision correction factors builds upon theprocess described above. As described above, the FRC is calibrated usinga MFC as a reference. The FRC is zeroed, and a previously verified MFC(preferably with N₂) is used. Subsequent to zeroing, each FRC channel isverified individually using the MFC as a reference, while the remainingchannels are closed using isolation valves. The resulting FRC readingsare used to calculate corrected set points based on the measured spanerror of each channel (See Equations 1 and 2).

Having derived the span correction factors (CF_(i)), gas-independentprecision correction factors can now be derived, making the FRCgas-independent. Equation 10 represents the calculation ofgas-independent precision correction factors for a 4-channel device,such as that shown in the embodiment of FIG. 3.

$\begin{matrix}{{{P\; C\; F_{1}} = \frac{4}{1 + {\frac{1}{C\; F_{1}}\left( {{C\; F_{2}} + {C\; F_{3}} + {C\; F_{4}}} \right)}}}{{P\; C\; F_{2}} = \frac{4}{1 + {\frac{1}{C\; F_{2}}\left( {{C\; F_{1}} + {C\; F_{3}} + {C\; F_{4}}} \right)}}}{{P\; C\; F_{3}} = \frac{4}{1 + {\frac{1}{C\; F_{3}}\left( {{C\; F_{1}} + {C\; F_{2}} + {C\; F_{4}}} \right)}}}{{P\; C\; F_{4}} = \frac{4}{1 + {\frac{1}{C\; F_{4}}\left( {{C\; F_{1}} + {C\; F_{2}} + {C\; F_{3}}} \right)}}}} & \left( {{Equation}\mspace{14mu} 10} \right)\end{matrix}$

Equation 10 allows the span correction factors (CF_(i)) to benormalized. After calculating the gas-independent precision correctionfactors (PCF_(i)) using Equation 10, it may be necessary for the host tostore these values in a table, and these values may need to beaccessible every time a new set point is set on the FRC, e.g., auser-input command for change in process conditions. Using thegas-independent precision correction factors (PCF_(i)), the correctedset points can be recalculated by substituting the gas-independentprecision correction factors (PCF_(i)) derived from Equation 10 for thespan correction factors (CF_(i)) of Equation 2, thus becominggas-independent. The result yields Equation 11.

$\begin{matrix}{{cSP}_{i} = {\frac{{SP}_{i}}{P\; C\; F_{i}}*\left( {\sum\limits_{i}^{n}\frac{{SP}_{i}}{P\; C\; F_{i}}} \right)^{- 1}}} & \left( {{Equation}\mspace{14mu} 11} \right)\end{matrix}$

In Equation 11, cSP_(i) represents the corrected set point for channeli, SP_(i) represents the set point for channel i, and PCF_(i) representsthe gas-independent precision correction factor for channel i, ascalculated from Equation 10.

The derivation of gas-independent precision correction factors (PCF_(i))also simplifies diagnostics and monitoring of the FRC. Specifically, thegas-independent precision correction factors (PCF_(i)) also allow thespan drift of channel i to be monitored, even when different processgases are used. The span drift of channel i is the change of thegas-independent precision span correction factors (PCF_(i)) of a channelof the FRC over time. Thus, the span drift is indicative of the FRC'sability to maintain a constant flow rate therethrough over time. Thespan drift is presented per unit time, thus allowing a user to form arecalibration or replacement schedule for the FRC. Since the span driftis determined using the gas-independent precision span correctionfactors (PCF_(i)), span drift can be monitored even when the FRC is usedto regulate the flow of multiple process gases for different processes.It should be apparent to one skilled in the art that it is not necessaryto control and regulate gas flow rates using the gas-independentprecision correction factors (PCF_(i)), but instead a process can becontrolled using use the span correction factors (CF_(i)). However, theuse of the gas-independent precision span correction factors (PCF_(i))provides for gas-independent monitoring and regulation.

Table 2 shows the resulting flow imbalances for uncorrected set points,as well as variations in QinRd based on set point. In one example ofTable 2, the total uncorrected flow balance can be off from the desiredflow balance by over 8 percent. In another example of Table 2, eventhough total flow balance is off less than one-tenth of a percent,individual channel flow rates may be off by more than 40 percent.Therefore, it is apparent that there is a need to correct errors in flowrate, preferably using a reduced amount of hardware.

As can be seen in Table 2, the FRC actual flow as measured by the MFCfor channel 1 was 100 SCCM of N₂ gas. However, the FRC read the incomingflow for channel 1 as 110 SCCM of N₂ gas, which resulted in an error of10 SCCM of N₂ gas through channel 1, and a span correction factor of0.909091. The FRC actual flow as measured by the MFC for channel 2 was98 SCCM of N₂ gas. The FRC read the incoming flow for channel 2 as 67SCCM of N₂ gas, which resulted in an error of 31 SCCM of N₂ gas throughchannel 2, generating a span correction factor of 0.89286 using Equation1.

The FRC actual flow as measured by the MFC for channel 3 was 100 SCCM ofN₂ gas. The FRC read the incoming flow for channel 3 as 180 SCCM of N₂gas, which resulted in an error of 80 SCCM of N₂ and a span correctionfactor of 0.55556. The FRC actual flow as measured by the MFC forchannel 4 was 100 SCCM of N₂ gas. The FRC read the incoming flow forchannel 4 as 112 SCCM of N₂ gas, which resulted in an error of 12 SCCMof N₂ gas and a span correction factor of 0.909091. The total flowthrough all four channels combined was 398 SCCM of N₂ gas, although theFRC was reading a flow rate of 469 SCCM of N₂ gas. This results in anerror of 71 SCCM of N₂ gas.

The second and third parts of Table 2 emphasize the importance ofchecking span correction factors, and calculating corrected set points.In the second part of Table 2, channels 1 through 4 are set at 20percent, 30 percent, 20 percent, and 30 percent, respectively. The totalincoming actual flow (QinActual) is 300 SCCM of N₂ gas, while the flowrate read by the FRC channels is (QinRd) is 300.1 SCCM of N₂ gas. Lowerrors in QinActual versus QinRd can occur in a number of circumstances.For example, when set points have previously been calculated for thisprocess, when set points have been calculated for a similar process, orwhen the flow rates are coincidentally equal. However, the third part ofTable 2 exemplifies the error in channel flow rate that can occur ifcorrected set points are not determined. Even though QinActual and QinRdwere approximately equal in part 2 of Table 2, QinActual and QinRd havea relatively large error upon changing the set points of the individualchannels, as in part 3 of Table 2.

In part 3 of Table 2, the set points for channels 1 through 4 arechanged to 10 percent, 40 percent, 10 percent, and 40 percent,respectively. Even though it appears from the second part of Table 2that the Single Channel Actual Flow and the Single Channel Reading areapproximately equal when looking at the overall gas flow (sinceQinActual and QinRd are approximately equal), Part 3 shows this is nottrue. By changing the set points of channels 1 through 4 in Part 3,QinActual and QinRd vary by about 8 percent, indicating the need toemploy corrected set points for channels 1 through 4.

If a process user relied solely on the QinActual and QinRd of the secondpart of Table 2, the process user may be lead to believe that the FRCsare accurate, because the overall flow rate is accurate. However, if theprocess user did not verify single channel span errors or correctionfactors, then any process recipe that deviated from that of part 2 ofTable 2 would not be accurate. These inaccuracies can createnon-uniformity amongst processed substrates, or my lead to unusablesubstrates. Therefore, it is important that all channels of the FRC becalibrated, and any errors be accounted for through the use of correctedset points.

TABLE 2 ch1 ch2 ch3 ch4 Total FRC Span Verification Single ChannelActual Flow (SCCM) 100 98 100 100 398 Single Channel Reading (SCCM) 11067 180 112 469 Reading Error 10 −31 80 12 71 Span Slope 1.1000000.683673 1.800000 1.120000 Span Correction Factor 0.909091 1.462690.55556 0.89286 Calculated Uncorrected Controlled Flow Set Point Percent20.00% 30.00% 20.00% 30.00% 100.00% Channel Actual Flow (SCCM) 54.6131.7 33.3 80.4 300 Channel Reading (SCCM) 60.0 90.0 60.0 90.0 300.1Calculated Uncorrected Controlled Flow Set Point Percent 10.00% 40.00%10.00% 40.00% 100.00% Channel Actual Flow (SCCM) 25.1 161.2 15.3 98.4300 Channel Reading (SCCM) 27.6 110.2 27.6 110.2 275.6

Although embodiments herein generally refer to the regulation andmonitoring of nitrogen (N₂) gas, it is contemplated that the flow of anyprocess may be controlled using the methods described herein.

Benefits of the present invention include the ability to measure andaccount for differences between the actual gas flow and the measured gasflow during substrate processing. Thus, a dual tandem processing chambermay be used to increase substrate throughput and process uniformity at areduced cost compared to a single substrate processing chamber.

While the foregoing is directed to embodiments of the present invention,other and further embodiments of the invention may be devised withoutdeparting from the basic scope thereof, and the scope thereof isdetermined by the claims that follow.

1. A method of calibrating a flow ratio controller for a tandem chamberhaving two process chambers, each process chamber having a gas diffusercomprising multiple gas zones disposed therein, each gas zone of eachgas diffuser coupled to the same process gas supply, comprising: a)setting a first channel of a flow ratio controller coupled to theprocess gas supply to a 100 percent set point; b) setting all remainingchannels of the flow ratio controller to a zero percent set point; c)closing all downstream isolation valves for the remaining channels ofthe flow ratio controller that are set at the zero percent set point; d)setting the flow of a mass flow controller equal to the flow of the 100percent set point of the first channel; e) stabilizing the flow of aprocess gas through the flow ratio controller; f) calculating a spancorrection factor for the flow of the process gas through the firstchannel of the flow ratio controller; g) calculating a span correctionfactor for the flow of the process gas through the remaining channels ofthe flow ratio controller, comprising individually setting the flowratio controller for each remaining channel to the 100 percent setpoint, and repeating elements (b)-(f) for each of the remainingchannels; and h) determining the corrected set point for each channel ofthe flow ratio controller.
 2. The method of claim 1, wherein thecorrected set point of each channel is determined using the equation:${{cSP}_{i} = {\frac{{SP}_{i}}{C\; F_{i}}*\left( {\sum\limits_{i}^{n}\frac{{SP}_{i}}{C\; F_{i}}} \right)^{- 1}}},$where cSP_(i) is the corrected set point of each channel, SP_(i) is aninitial set point for each channel; and CF_(i) is the span correctionfactor for each channel.
 3. The method of claim 1, further comprisingrecording a reported flow of the process gas through a mass flowcontroller and the flow ratio controller.
 4. The method of claim 2,further comprising zeroing the flow ratio controller channels.
 5. Themethod of claim 4, wherein the process gas supply comprises a nitrogengas supply.
 6. The method of claim 4, wherein a channel flow readingthrough any of the channels of the flow ratio controller is between 80percent and 100 percent of a maximum flow rate through the channel. 7.The method of claim 4, wherein the stabilizing the flow comprisesflowing the process gas through the flow ratio controller for at leastabout 50 seconds.
 8. The method of claim 7, wherein calculating a spancorrection factor comprises determining a mean flow rate of the processgas through the flow ratio controller based upon at least 10 evenlytime-spaced samples.
 9. The method of claim 2, further comprisingapplying a precision correction factor to make the flow ratio controllergas-independent, wherein the precision correction factors are used todetermine the corrected set points with the following equation:${{cSP}_{i} = {\frac{{SP}_{i}}{P\; C\; F_{i}}*\left( {\sum\limits_{i}^{n}\frac{{SP}_{i}}{P\; C\; F_{i}}} \right)^{- 1}}},$where cSP_(i) is the corrected set point for each channel, SP_(i) is theinitial set point for each channel, and PCF_(i) is the precision spancorrection factor.
 10. The method of claim 9, wherein the flow ratiocontroller comprises at least two channels.
 11. A method of calibratinga flow ratio controller for a tandem etching chamber, the flow ratiocontroller having a plurality of channels coupled to a process gassupply source, comprising: determining a span correction factor for afirst channel of the flow ratio controller, comprising: setting thefirst channel of the flow ratio controller to a 100 percent set point;setting all remaining channels of the flow ratio controller to a zeropercent set point; closing all downstream isolation valves for theremaining channels of the flow ratio controller that are set to the zeropercent set point; setting the flow of a mass flow controller equal tothe flow of the 100 percent set point of the first channel; stabilizingthe flow of a process gas through the first channel of the flow ratiocontroller; measuring the flow of the process gas through the firstchannel of the flow ratio controller for at least 10 evenly-spacedsamples; and calculating a span correction factor for the flow of theprocess gas through the first channel of the flow ratio controller;determining a span correction factor for the remaining channels of theplurality of channels of the flow ratio controller; and determining thecorrected set points for each channel of the flow ratio controller usingthe equation:${{cSP}_{i} = {\frac{{SP}_{i}}{C\; F_{i}}*\left( {\sum\limits_{i}^{n}\frac{{SP}_{i}}{C\; F_{i}}} \right)^{- 1}}},$where cSP_(i) is the corrected set point of each channel, SP_(i) is aninitial set point for each channel; and CF_(i) is the span correctionfactor for each channel.
 12. The method of claim 11, wherein measuringthe flow of the process gas through the first channel further comprisesdetermining a mean flow rate of the process gas through the firstchannel based on the at least 10 evenly-spaced samples.
 13. The methodof claim 11, further comprising zeroing the flow ratio controller. 14.The method of claim 11, further recalculating the corrected set pointsfor each channel of the flow ratio controller using the equation:${{cSP}_{i} = {\frac{{SP}_{i}}{P\; C\; F_{i}}*\left( {\sum\limits_{i}^{n}\frac{{SP}_{i}}{P\; C\; F_{i}}} \right)^{- 1}}},$where cSP_(i) is the corrected set point for each channel, SP_(i) is theinitial set point for each channel, and PCF_(i) is a precision spancorrection factor.
 15. The method of claim 14, wherein the flow ratiocontroller comprises at least four channels.
 16. A method of calibratinga flow ratio controller for a tandem etching chamber, comprising:flowing a process gas into four gas supply lines, a first gas line andsecond gas line coupled to a first process chamber, and a third gas lineand fourth gas line coupled to a second process chamber, each gas linecoupled to a distinct channel of a flow ratio controller; determining acorrected set point for the first, second, third, and fourth channels ofthe flow ratio controller, the corrected set points calculated using theequation:${{cSP}_{i} = {\frac{{SP}_{i}}{C\; F_{i}}*\left( {\sum\limits_{i}^{n}\frac{{SP}_{i}}{C\; F_{i}}} \right)^{- 1}}},$where cSP_(i) is the corrected set point of each channel, SP_(i) is aninitial set point for each channel; and CF_(i) is the span correctionfactor for each channel; determining gas-independent precisioncorrection factors for the first, second, third, and fourth channels ofthe flow ratio controller using the equations:${P\; C\; F_{1}} = \frac{4}{1 + {\frac{1}{C\; F_{1}}\left( {{C\; F_{2}} + {C\; F_{3}} + {C\; F_{4}}} \right)}}$${P\; C\; F_{2}} = \frac{4}{1 + {\frac{1}{C\; F_{2}}\left( {{C\; F_{1}} + {C\; F_{3}} + {C\; F_{4}}} \right)}}$${P\; C\; F_{3}} = \frac{4}{1 + {\frac{1}{C\; F_{3}}\left( {{C\; F_{1}} + {C\; F_{2}} + {C\; F_{4}}} \right)}}$${{P\; C\; F_{4}} = \frac{4}{1 + {\frac{1}{C\; F_{4}}\left( {{C\; F_{1}} + {C\; F_{2}} + {C\; F_{3}}} \right)}}},$where PCF₁, PCF₂, PCF₃, and PCF₄ are the precision span correctionfactors for the first, second, third, and fourth channels, and CF₁, CF₂,CF₃, and CF₄, are the span correction factors for the first, second,third, and fourth channels; and recalculating the corrected set pointsfor the first, second, third, and fourth channels of the flow ratiocontroller using the gas-independent precision correction factors andthe equation:${{cSP}_{i} = {\frac{{SP}_{i}}{P\; C\; F_{i}}*\left( {\sum\limits_{i}^{n}\frac{{SP}_{i}}{P\; C\; F_{i}}} \right)^{- 1}}},$where cSP_(i) is the corrected set point for each channel, SP_(i) is theinitial set point for each channel, and PCF_(i) is the gas-independentprecision span correction factor for each channel.
 17. The method ofclaim 16, wherein the first process chamber and the second processchamber are adapted to each process a substrate simultaneously.
 18. Themethod of claim 17, wherein the first process chamber and the secondprocess chamber are adapted to process the substrates undersubstantially the same operating conditions.
 19. The method of claim 18,wherein the determining the corrected set point for the first channel ofthe flow ratio controller comprises: setting the first channel of a flowratio controller to a 100 percent set point; setting the second, thirdand fourth channels of the flow ratio controller to a zero percent setpoint; closing all downstream isolation valves for the second, third,and fourth channels of the flow ratio controller; setting the flow of amass flow controller equal to the flow of the 100 percent set point ofthe first channel; stabilizing the flow of a process gas through theflow ratio controller; calculating a span correction factor for the flowof the process gas through the first channel of the flow ratiocontroller; and calculating the corrected set point of the first channelof the flow ratio controller.
 20. The method of claim 19, furthercomprising determining the a span drift of at least one of the first,second, third, or fourth channels, wherein the span drift is defined asthe gas-independent precision correction factor at a first time minusthe gas-independent precision span correction factor at a second time,divided by the length of time between the first time and the secondtime.